Finite Group Databasebeta

← C11×#36635 #14613828

Subgroups — C11×#36635 #14613828

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2864C212yesmaximal, complemented
2C11×#2863C214yesmaximal, complemented
3C11×#2862C211yesmaximal, characteristic, complemented
4C11×#2859C211yesmaximal, characteristic, complemented
5C11×#2857C212yesmaximal
6C11×#2855C214yesmaximal
7C11×#2851C212yesmaximal
8C4×C11×C4⋊Q8C212yesmaximal, complemented
9C4×C11×#125C212yesmaximal, complemented
10C4×C11×C22⋊Q8C214yesmaximal
11C11×#2295C214yesmaximal, complemented
12C11×#2283C212yesmaximal
13C2×C43×C11C211yesmaximal, characteristic
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×#125C2212yes—
16C2×C11×C22⋊Q8C2214yes—
17C2×C4×Q8×C11C2214yes—
18C22×C42×C11C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2212yes—
21C22×C42×C11C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C11×#391C2214yes—
24C11×#391C2214yes—
25C11×#391C2214yes—
26C11×#391C2214yes—
27C11×#389C2214yes—
28C11×#389C2214yes—
29C11×#389C2214yes—
30C11×#389C2214yes—
31C11×#389C2214yes—
32C11×#389C2214yes—
33C11×#387C2218yes—
34C11×#387C2218yes—
35C11×#387C2218yes—
36C11×#387C2218yes—
37C11×#385C2218yes—
38C11×#384C2212yes—
39C11×#383C2214yes—
40C11×#382C2212yes—
41C11×#382C2212yes—
42C11×#382C2212yes—
43C11×#381C2214yes—
44C11×#380C2214yes—
45C11×#380C2214yes—
46C4×C11×C4⋊C4C2214yes—
47C4×C11×C4⋊C4C2218yes—
48C4×C11×C4⋊C4C2214yes—
49C4×C11×C22⋊C4C2214yes—
50C11×#376C2214yes—
51C43×C11C2212yes—
52C43×C11C2211yescharacteristic
53C43×C11C2211yescharacteristic
54C43×C11C2211yescharacteristic
55C43×C11C2212yes—
56C43×C11C2211yescharacteristic
57C22×Q8×C11C2314yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C11×C4⋊Q8—28no—
64C11×#125—28no—
65C11×C22⋊Q8—216no—
66C4×Q8×C11—216no—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2318yes—
72C2×C11×C4⋊C4C2318yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2318yes—
75C2×C11×C22⋊C4C2318yes—
76C2×C42×C11—28no—
77C2×C42×C11—28no—
78C2×C42×C11—24no—
79C2×C42×C11—24no—
80C2×C42×C11Q818yescomplemented
81C2×C42×C11C2312yes—
82C2×C42×C11C2312yes—
83C2×C42×C11C2312yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2312yes—
88C2×C42×C11C2312yes—
89C2×C42×C11C2312yes—
90C2×C42×C11C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2318yes—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2312yes—
100C11×#95C2318yes—
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11×#95C2314yes—
104C11×#95C2314yes—
105C11×#95C2318yes—
106C11×#95C2318yes—
107C11×#95C2318yes—
108C11×#95C2318yes—
109#36635C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11C2411yescharacteristic
111C2×Q8×C11—28no—
112C2×Q8×C11—28no—
113C2×Q8×C11—28no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C2×Q814yes—
124C22×C4×C11C2×Q814yes—
125C22×C4×C11C2×Q814yes—
126C22×C4×C11#4118yes—
127C22×C4×C11C2418yes—
128C22×C4×C11C2418yes—
129C22×C4×C11C2411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×C4×C11C2412yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2411yescharacteristic
137C22×C4×C11C2412yes—
138C22×C4×C11C2411yescharacteristic
139C11×C4⋊C4—28no—
140C11×C4⋊C4—216no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—216no—
143C11×C4⋊C4—216no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—28no—
147C11×C22⋊C4—216no—
148C42×C11—24no—
149C42×C11—24no—
150C42×C11—24no—
151C42×C11—24no—
152C42×C11—24no—
153C42×C11—24no—
154C42×C11—24no—
155C42×C11—24no—
156C42×C11—24no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—216no—
160C42×C11C2×Q814yes—
161C42×C11C2×Q814yes—
162C42×C11C2×Q814yes—
163C42×C11C2×Q814yes—
164C42×C11#4118yes—
165C42×C11#4114yes—
166C42×C11#4114yes—
167#2864C2×C1112yescomplemented
168#2863C2×C1114yescomplemented
169#2862C2×C1111yescharacteristic, complemented
170#2859C2×C1111yescharacteristic, complemented
171#2857C2×C1112yes—
172#2855C2×C1114yes—
173#2851C2×C1112yes—
174C4×C4⋊Q8C2×C1112yescomplemented
175C4×#125C2×C1112yescomplemented
176C4×C22⋊Q8C2×C1114yes—
177#2295C2×C1114yescomplemented
178#2283C2×C1112yes—
179C2×C43C2×C1111yescharacteristic
180C23×C11—21no—
181C23×C11—22no—
182C23×C11—21no—
183C23×C11C22×Q812yes—
184C23×C11C2×#4114yes—
185C23×C11C2511yescharacteristic
186Q8×C11—416no—
187C2×C4×C11—216no—
188C2×C4×C11—28no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—216no—
201C2×C4×C11—28no—
202C2×C4×C11—28no—
203C2×C4×C11—28no—
204C2×C4×C11—28no—
205C2×C4×C11—28no—
206C2×C4×C11—28no—
207C2×C4×C11—28no—
208C2×C4×C11—28no—
209C2×C4×C11C22×Q812yes—
210C2×C4×C11C22×Q812yes—
211C2×C4×C11C22×Q812yes—
212C2×C4×C11C22×Q812yes—
213C2×C4×C11C22×Q812yes—
214C2×C4×C11C22×Q812yes—
215C2×C4×C11C2×#4114yes—
216C2×C4×C11C2×#4114yes—
217C2×C4×C11C2×#4114yes—
218C2×C4×C11C2×#4114yes—
219C2×C4×C11C2×#4114yes—
220C2×C4×C11C2×#4114yes—
221C2×C4×C11C2×#4114yes—
222C2×C4×C11C2×#4112yes—
223C2×C4×C11C2×#4112yes—
224C2×C4⋊Q8C22×C1112yes—
225C2×#125C22×C1112yes—
226C2×C22⋊Q8C22×C1114yes—
227C2×C4×Q8C22×C1114yes—
228C22×C42C22×C1111yescharacteristic
229C22×C42C22×C1112yes—
230C22×C42C22×C1111yescharacteristic
231C22×C42C22×C1112yes—
232C22×C42C22×C1111yescharacteristic
233#391C22×C1114yes—
234#391C22×C1114yes—
235#391C22×C1114yes—
236#391C22×C1114yes—
237#389C22×C1114yes—
238#389C22×C1114yes—
239#389C22×C1114yes—
240#389C22×C1114yes—
241#389C22×C1114yes—
242#389C22×C1114yes—
243#387C22×C1118yes—
244#387C22×C1118yes—
245#387C22×C1118yes—
246#387C22×C1118yes—
247#385C22×C1118yes—
248#384C22×C1112yes—
249#383C22×C1114yes—
250#382C22×C1112yes—
251#382C22×C1112yes—
252#382C22×C1112yes—
253#381C22×C1114yes—
254#380C22×C1114yes—
255#380C22×C1114yes—
256C4×C4⋊C4C22×C1114yes—
257C4×C4⋊C4C22×C1118yes—
258C4×C4⋊C4C22×C1114yes—
259C4×C22⋊C4C22×C1114yes—
260#376C22×C1114yes—
261C43C22×C1111yescharacteristic
262C43C22×C1111yescharacteristic
263C43C22×C1111yescharacteristic
264C43C22×C1112yes—
265C43C22×C1111yescharacteristic
266C43C22×C1112yes—
267C22×C11—24no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—24no—
271C22×C11#53314yes—
272C22×C11C23×Q811yescharacteristic
273C22×C11C22×#4111yescharacteristic
274C22×C11C22×#4112yes—
275C22×C11C22×#4112yes—
276C22×C11C22×#4111yescharacteristic
277C4×C11—24no—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—24no—
283C4×C11—24no—
284C4×C11—48no—
285C4×C11—48no—
286C4×C11#52918yes—
287C4×C11#53314yes—
288C4×C11#53314yes—
289C22×Q8C23×C1114yes—
290C23×C4C23×C1112yes—
291C23×C4C23×C1111yescharacteristic
292C23×C4C23×C1111yescharacteristic
293C23×C4C23×C1111yescharacteristic
294C23×C4C23×C1112yes—
295C4⋊Q8—28no—
296#125—28no—
297C22⋊Q8—216no—
298C4×Q8—216no—
299C2×C4⋊C4C23×C1114yes—
300C2×C4⋊C4C23×C1118yes—
301C2×C4⋊C4C23×C1114yes—
302C2×C4⋊C4C23×C1118yes—
303C2×C4⋊C4C23×C1114yes—
304C2×C4⋊C4C23×C1118yes—
305C2×C4⋊C4C23×C1114yes—
306C2×C4⋊C4C23×C1114yes—
307C2×C22⋊C4C23×C1118yes—
308C2×C42—28no—
309C2×C42—28no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42Q8×C1118yescomplemented
313C2×C42C23×C1118yes—
314C2×C42C23×C1112yes—
315C2×C42C23×C1112yes—
316C2×C42C23×C1112yes—
317C2×C42C23×C1112yes—
318C2×C42C23×C1112yes—
319C2×C42C23×C1111yescharacteristic
320C2×C42C23×C1111yescharacteristic
321C2×C42C23×C1112yes—
322C2×C42C23×C1112yes—
323C2×C42C23×C1112yes—
324C2×C42C23×C1112yes—
325C2×C42C23×C1111yescharacteristic
326C2×C42C23×C1111yescharacteristic
327C2×C42C23×C1111yescharacteristic
328C2×C42C23×C1111yescharacteristic
329C2×C42C23×C1112yes—
330C2×C42C23×C1111yescharacteristic
331C2×C42C23×C1111yescharacteristic
332#95C23×C1118yes—
333#95C23×C1114yes—
334#95C23×C1114yes—
335#95C23×C1114yes—
336#95C23×C1114yes—
337#95C23×C1118yes—
338#95C23×C1118yes—
339#95C23×C1118yes—
340#95C23×C1118yes—
341C2×C11—24no—
342C2×C11C2×#52912yes—
343C2×C11C2×#53311yescharacteristic
344C2×C11C2×#53311yescharacteristic
345C2×C11C2×#53311yescharacteristic
346C2×C11#344412yes—
347C24C24×C1111yescharacteristic
348C2×Q8—28no—
349C2×Q8—28no—
350C2×Q8—28no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4C2×Q8×C1114yes—
361C22×C4C2×Q8×C1114yes—
362C22×C4C2×Q8×C1114yes—
363C22×C4C11×#4118yes—
364C22×C4C24×C1118yes—
365C22×C4C24×C1118yes—
366C22×C4C24×C1111yescharacteristic
367C22×C4C24×C1111yescharacteristic
368C22×C4C24×C1111yescharacteristic
369C22×C4C24×C1111yescharacteristic
370C22×C4C24×C1112yes—
371C22×C4C24×C1112yes—
372C22×C4C24×C1112yes—
373C22×C4C24×C1111yescharacteristic
374C22×C4C24×C1111yescharacteristic
375C22×C4C24×C1112yes—
376C4⋊C4—28no—
377C4⋊C4—216no—
378C4⋊C4—28no—
379C4⋊C4—216no—
380C4⋊C4—216no—
381C4⋊C4—28no—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C22⋊C4—216no—
385C42—24no—
386C42—24no—
387C42—24no—
388C42—24no—
389C42—24no—
390C42—24no—
391C42—24no—
392C42—24no—
393C42—24no—
394C42—22no—
395C42—22no—
396C42—216no—
397C42C2×Q8×C1114yes—
398C42C2×Q8×C1114yes—
399C42C2×Q8×C1114yes—
400C42C2×Q8×C1114yes—
401C42C11×#4118yes—
402C42C11×#4114yes—
403C42C11×#4114yes—
404C11#3663511yescharacteristic, direct product factor, Sylow
405C23—21no—
406C23—22no—
407C23—21no—
408C23C22×Q8×C1112yes—
409C23C2×C11×#4114yes—
410C23C25×C1111yescharacteristic
411Q8—416no—
412C2×C4—216no—
413C2×C4—28no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—216no—
426C2×C4—28no—
427C2×C4—28no—
428C2×C4—28no—
429C2×C4—28no—
430C2×C4—28no—
431C2×C4—28no—
432C2×C4—28no—
433C2×C4—28no—
434C2×C4C22×Q8×C1112yes—
435C2×C4C22×Q8×C1112yes—
436C2×C4C22×Q8×C1112yes—
437C2×C4C22×Q8×C1112yes—
438C2×C4C22×Q8×C1112yes—
439C2×C4C22×Q8×C1112yes—
440C2×C4C2×C11×#4114yes—
441C2×C4C2×C11×#4114yes—
442C2×C4C2×C11×#4114yes—
443C2×C4C2×C11×#4114yes—
444C2×C4C2×C11×#4114yes—
445C2×C4C2×C11×#4114yes—
446C2×C4C2×C11×#4114yes—
447C2×C4C2×C11×#4112yes—
448C2×C4C2×C11×#4112yes—
449C22—24no—
450C22—22no—
451C22—22no—
452C22—24no—
453C22C11×#53314yes—
454C22C23×Q8×C1111yescharacteristic
455C22C22×C11×#4111yescharacteristic
456C22C22×C11×#4112yes—
457C22C22×C11×#4112yes—
458C22C22×C11×#4111yescharacteristic
459C4—24no—
460C4—22no—
461C4—22no—
462C4—22no—
463C4—22no—
464C4—24no—
465C4—24no—
466C4—48no—
467C4—48no—
468C4C11×#52918yes—
469C4C11×#53314yes—
470C4C11×#53314yes—
471C2—24no—
472C2C2×C11×#52912yes—
473C2C2×C11×#53311yescharacteristic
474C2C2×C11×#53311yescharacteristic
475C2C2×C11×#53311yescharacteristic
476C2C11×#344412yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC24×C11C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#2864C2semidirect
2. C11×#2863C2semidirect
3. C11×#2862C2semidirect
4. C11×#2859C2semidirect
8. C4×C11×C4⋊Q8C2semidirect
9. C4×C11×#125C2semidirect
11. C11×#2295C2semidirect
80. C2×C42×C11Q8semidirect
109. #36635C11direct (N × H)
167. #2864C2×C11semidirect
168. #2863C2×C11semidirect
169. #2862C2×C11semidirect
170. #2859C2×C11semidirect
174. C4×C4⋊Q8C2×C11semidirect
175. C4×#125C2×C11semidirect
177. #2295C2×C11semidirect
312. C2×C42Q8×C11semidirect
404. C11#36635direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#28642
C11×#28632
C11×#28622
C11×#28592
C11×#28572
C11×#28552
C11×#28512
C4×C11×C4⋊Q82
C4×C11×#1252
C4×C11×C22⋊Q82
C11×#22952
C11×#22832
C2×C43×C112
#3663511